Charles studied the compressibility of gases nearly a century
after Boyle. In his experiments he observed "At a fixed
pressure, the volume of a gas is proportional to the temperature
of the gas." The experiment is simple: (see figure on left)

A cylinder with a piston and a gas is immersed in a bath (e.g.
water). A mass is placed on top of the piston which results in
a pressure on the gas. This mass is held constant which means
that the pressure on the gas is constant. The gas volume is measured
as the temperature is increased and V vs T data point plotted.
This is continued over a large range of temperatures. To see
what happens place the mouse cursor over the image.

The straight line implies

which suggests we define a new temperature T (the kelvin
temperature scale) as

which leads to

Which is Charle's law (P and n constant)

Example: In the experiment above the initial volume and temperature
of the gas is 0.5L, 5 0C. Assuming the pressure and moles of
gas is constant, what is the volume of the gas if the temperature
is increased to 80 0C? Let T1 and V1 be the initial temperature
and volume and let T2, V2 be the final temperature and volume.
Then according to Charles law,